Mostly the Emails are stored with the Email provider.
If you by any chance have a CSV file with all emails it would be possible to import them into Hubspot like any other activity. Here ia a quick overview on how to do it: Is it possible to import activities to Hubspot with your tool?
Unfortunalely, at the moment do not have email sync capability directly from Gmail or Outlook.
We will let you know in case we come up with the solution to this problem.
Here is a quick video overview on how to bulk import emails to Hubspot: